The Elementary Divisors, Associated with 0, of a Singular M-matrix

Author:

Schneider Hans

Abstract

1. Many investigations have been concerned with a squaro matrix P with non-negative coefficients (elements). It is remarkable that many interesting properties of P are determined by the set Σ of index pairs of positive (i.e. non-zero) coefficients of P, the actual values of these coefficients being irrelevant. Thus, for example, the number of characteristic roots equal in absolute value to the largest non-negative characteristic root p depends on Σ alone, if P is irreducible. If P is reducible, then Σ determines the standard forms of P (cf. § 3). The multiplicity of p depends on Σ, and on the set S of indices of those submatrices in the diagonal in a standard form of P which have p as a characteristic root. It has apparently not been considered before whether Σ and S also determine the elementary divisors associated with p. We shall show that, in general, the elementary divisors do not depend on these sets alone, but that necessary and sufficient conditions may be found in terms of Σ and S (a) for the elementary divisors associated with p to be simple, and (b) that there is only one elementary divisor associated with p.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference8 articles.

1. An Inequality for Latent Roots Applied To Determinants with Dominant Principal Diagonal

2. �ber die determinanten mit �berwiegender Hauptdiagonale

3. Ueber das Nichtversclnnnden einer Klasso von Determinanten und die Lokalisierung der charakteristischen Wurzeln von Matrizen;Ostrowski;Compositio Math.,1951

4. Bounds for characteristic roots of matrices II

5. Unzerlegbare, nicht negative Matrizen

Cited by 53 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Matrices Leaving a Cone Invariant;Discrete Mathematics and Its Applications;2013-11-26

2. Nonnegative Matrices and Stochastic Matrices;Discrete Mathematics and Its Applications;2013-11-26

3. Special families of matrices – A talk in honor of Miroslav Fiedler;Linear Algebra and its Applications;2013-08

4. Z-matrix equations in max-algebra, nonnegative linear algebra and other semirings;Linear and Multilinear Algebra;2012-10

5. Is ACn,n a general H-matrix?;Linear Algebra and its Applications;2012-01

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3